No. That is, if you are a shareholder of a closely-held company or business you do not need the physical stock certificate to enforce your rights as a shareholder. New York law specifically addresses this point and NY Business Corporation Law Section 504(i), states:
When consideration is paid and shares of stock are purchased, the purchaser “…shall be entitled to all the rights and privileges of a holder of such shares and to a certificate representing his shares…”
So, provided that you pay for your stock and equity interest, the failure of your “partners” to actually issue a physical certificate to you will not ordinarily defeat your rights as an owner.